Project abstract for group elliotrs

Materials Modeling, From Multiple Scales, of Instabilities and Bifurcation

The Elliott research group looks at bifurcation and stability problems of complex materials and structural systems. Problems of interest include solid-to-solid phase transitions, hierarchical materials such as honeycomb structures, nano-structures such as nanotubes, and complex nano-clusters. The group develops and uses rigorous computational algorithms based on continuation and bifurcation theory that take advantage of group-theory results to systematically map out equilibrium configurations for the models considered. Models are developed and drawn from multiple physical length scales and include electronic structure density functional theory (ES-DFT), emperical atomistic modeling, continuum mechanics, and structural beam theory.

Ongoing work involves the development and extension of the group's branch-following and bifurcation (BFB) methodology to support high-performance systems in a heterogeneous (possibly cloud-based) computing environment; development, testing, and application of next-generation ES-DFT codes; coupling commercial finite element method (FEM) codes to empirical atomistic models to study solid-to-solid phase transitions; and design of multi-state architectured materials using BFB and FEM technologies.